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Summary

This text for the one semester applied or business calculus course uses intriguing real-world applications to engage students' interest and show them the practical side of calculus. Many applications are financial or business related, but many applications in this text cover general-interest topics as well, including the growing population of Africa, the composition of the Supreme Court, water shortage, the fastest pitch in baseball, and pollution and the depletion of natural resources. The Fifth Edition maintains the hallmark features that have made Brief Applied Calculus so popular: contemporary and interesting applications; careful and effective use of technology, including integrated calculator coverage that is optional; constant pedagogical reinforcement through section summaries, chapter summaries, carefully annotated examples, and extra practice problems; and a variety of exercises and assignment options including exercise sets, projects, and essays.

Table of Contents

Preface

A User's Guide to Features

Integrating Excel

Graphing Calculator Terminology

Functions

Real Numbers, Inequalities, and Lines

Exponents

Functions

Functions, Continued

Derivatives and Their Uses

Limits and Continuity

Rates of Change, Slopes, and Derivatives

Some Differentiation Formulas

The Product and Quotient Rules

Higher-Order Derivatives

The Chain Rule and the Generalized Power Rule

Nondifferentiable Functions

Further Applications of Derivatives

Graphing Using the First Derivative

Graphing Using the and Second Derivatives

Optimization

Further Applications of Optimization

Optimizing Lot Size and Harvest Size

Implicit Differentiation and Related Rules

Exponential and Logarithmic Functions

Exponential Functions

Logarithmic Functions

Differentiation of Logarithmic and Exponential Functions

Two Applications to Economics: Relative Rates and Elasticity of Demand

Integration and Its Applications

Antiderivatives and Indefinite Integrals

Integration Using Logarithmic and Exponential Functions

Definite Integrals and Areas

Further Applications of Definite Integrals: Average Value and Area Between Curves

Two Applications to Economics: Consumers' Surplus and Income Distribution

Integration by Substitution

Integration Techniques and Differential Equations

Integration by Parts

Integration Using Tables

Improper Integrals

Numerical Integration

Differential Equations

Further Applications of Differential Equations: Three Models of Growth